WO 02/09480 has already disclosed an operating method and a system for the resonant operation of high-pressure lamps in longitudinal mode. Specified there is a method for finding the second longitudinal acoustic resonant frequency. It assumes that during the continuous sweeping of the frequency range including the longitudinal mode the resonant frequency in the vertical operating position can be found by an occurrence of a relative increase in the operating voltage of the lamp. It emerges that the longitudinal frequency for a segregated arc state is found in vertical resonance with the aid of this method, and then maintained. However, depending on the composition of the metal halide filling and the timing of the expiry of the search procedure, this frequency thus found can be established far too high, and so an excitation of the acoustic resonance at the frequency found with the aid of the abovemetioned method produces an inadequate mixing and does not eliminate the segregation satisfactorily. However, it is expensive to implement in an electronic ballast.